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Signal&System Jurusan Elektro STT Telkom 1/10 EE2423 SINYAL & SISTEM DERET FOURIER WAKTU KONTINU (DFWK) TEAM DOSEN

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Signal&System Jurusan Elektro STT Telkom 2/10 Deret Fourier Waktu Kontinu (DFWK) a 0, a k, b k : Fourier coefficients. k : harmonic number, T : period, = 2 /T For all t but discontinuities (signal average over a period, i.e. DC term & zero-frequency component.) analysis synthesis

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Signal&System Jurusan Elektro STT Telkom 3/10 Deret Fourier Waktu Kontinu (DFWK) synthesis DFS defined as: analysis Deret Fourier Bentuk Eksponensial Kompleks Bentuk ini lebih memberikan banyak informasi, karena koefisien Fourier dinyatakan secara eksplisit Link to FS real coeffs.

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Signal&System Jurusan Elektro STT Telkom 4/10 Spektral Fourier phase amplitude

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Signal&System Jurusan Elektro STT Telkom 5/10 DFWD Diskret square wave. amplitude phase

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Signal&System Jurusan Elektro STT Telkom 6/10 Fourier analysis - tools Input Time Signal Frequency spectrum Discrete DFS Periodic (period T) Continuous DTFT Aperiodic Discrete DFT ** Calculated via FFT ** Periodic (period T) Discrete ContinuousFT Aperiodic FS Continuous Note: j = -1, = 2 /T, s[n]=s(t n ), N = No. of samples

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Signal&System Jurusan Elektro STT Telkom 7/10 FS convergence s(t) piecewise-continuous; s(t) piecewise-monotonic; s(t) absolutely integrable, (a) (b) (c) Dirichlet conditions In any period: Example: square wave (a)(b)(c) if s(t) discontinuous then |a k | 0) Rate of convergence

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Signal&System Jurusan Elektro STT Telkom 8/10 Sifat-sifat Deret Fourier Diberikan dua sinyal periodik dengan period T dan fundamental frequency 0 =2/T sama: Linearity: Time-Shifting: Time-Reversal (Flip): Time-Scaling:

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Signal&System Jurusan Elektro STT Telkom 9/10 Sifat-sifat Deret Fourier (cont’d) Differentiation: Integration: Dekomposisi Genap-Ganjil dari Sinyal Real: Multiplication:

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Signal&System Jurusan Elektro STT Telkom 10/10 Tabel FS properties Time Frequency Homogeneity a·s(t) a·S(k) Additivity s(t) + u(t) S(k)+U(k) Linearity a·s(t) + b·u(t) a·S(k)+b·U(k) Time reversal s(-t) S(-k) Multiplication * s(t)·u(t) Convolution * S(k)·U(k) Time shifting Frequency shifting S(k - m)

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